The Connectivity Matrix: A Toolbox for Monitoring Bonded Atoms and Bonds

Hyperhardness and hypersoftness of atoms and their ions

CONTEXT

The theory of reactivity based on cDFT has been supplemented with the new method of calculating the atomic and local indices. With the use of previously derived relationship of the electron density gradient to the softness kernel and to the linear response function, we deliver theoretical analysis to obtain significant reactivity indices-the electron density derivatives: local softness and local hypersoftness together with the global hyperhardness index and the derivative of the global softness with respect to the number of electrons. The local derivatives have been applied in the calculation of responses of atoms to perturbation by an external potential by the alchemical approach. The vital role of the local softness has been confirmed; the potential role of the hypersoftness has been indicated.

METHOD

Our original theoretical scheme has been numerically illustrated with the results obtained with electron density calculations with B3LYP method implemented in Gaussian 16 package. The aug-cc-pvqz basis set has been routinely applied, except for the Ca atom (cc-pvqz). Using the pVTZ basis set recommended by Sadlej was necessary for the potassium atom.

From the Electron Density Gradient to the Quantitative Reactivity Indicators: Local Softness and the Fukui Function

Important reactivity measures such as the local softness, the Fukui function, and the global hardness have been calculated directly from first principles with the use of the electron density function, beyond the finite difference approximation. Our recently derived density gradient theorem and the principle of nearsightedness of the electronic matter have been instrumental in obtaining the original, albeit approximate, result on the local softness of an atom. By integration of the local softness s(r), we obtain the global softness S and the Fukui function f(r) = s(r)/S. Local and global softness values have also been calculated analytically for the basic hydrogenic orbitals; the general relation to the atomic number S = σZ ^-2 has been demonstrated, with constants σ characteristic for each orbital type. Global hardness η = 1/S calculated for atoms and ions has been favorably tested against its conventional measure given by the finite difference approximation: (I - A). Calculated test results for atoms and ions in rows 1-4 of the periodic table have been presented.